Slice all onions into uniform 1/4 inch rings, separating the layers for even cooking.

Heat 3 tablespoons of butter in a large heavy-bottomed skillet over medium-high heat until melted and foaming subsides. Add sliced onions, 1 teaspoon salt, and 1/2 teaspoon black pepper and stir to coat.

Reduce heat to medium and cook the onions, stirring occasionally, for 25 to 30 minutes until deeply golden brown and very tender.

Push the caramelized onions to one side of the skillet and add the remaining 1 tablespoon of butter to the cleared space. Sprinkle 2 tablespoons of flour over the butter and stir constantly for 1 to 2 minutes until light golden.

Slowly pour the warmed milk or cream into the roux in a thin stream while whisking constantly to prevent lumps, fully incorporating the liquid.

Stir the onions back into the sauce, add 1/2 teaspoon mustard powder and a pinch of nutmeg, and cook for 2 to 3 minutes over medium heat until smooth and silky.

If a thicker sauce is desired, whisk in the cornstarch slurry and simmer for 1 minute more, stirring constantly until the sauce thickens.

Taste the creamed onions and adjust seasoning with additional salt, pepper, or nutmeg as needed.

Transfer the creamed onions to a serving dish, garnish with chopped parsley, and serve warm as a side dish.